Buffer-Gas Loading Prospects for Molecular Oxygen
6.2 Optical detection
6.2.2 Detection in the atmospheric A band
The oxygen A band belongs to the group of the so-called visible atmospheric bands, which arise from rotational-vibrational transitions between the electronic ground state and the singlet b1Σ+g state. Due to the large vibrational constants of molecular oxygen, they separate into distinct series characterized by their respective vibrational quantum numbers, as listed in Table 6.4.
Lines in the A band of16O2 with spectral intensities above 10−20MHz/cm−2 per molecule are shown in Figure 6.5. They have been extracted from the HI-TRAN database [101], which lists them for a temperature of 296 K. The values have been converted to liquid nitrogen and liquid helium temperatures with equation (4.19) and the temperature dependent partition sum
Q(T) = 0.315097 + 0.735537T−6.32290·10−5 T2+ 1.25414·10−7 T3 (6.1) which takes T in Kelvin. It has been fitted to values supplied in the HITRAN database and gives high accuracy results between 70 and 500 K. The validity of an extrapolation of the curve to temperatures below 70 K of course is question-able, but should nonetheless be useful to indicate the strongest lines. As Figure 6.5 demonstrates, the spectrum narrows at lower temperatures as expected, un-til only a few lines remain. This results from a decreasing thermal population of higher rotational levels in the electronic ground state.
Since the b1Σ+g ← X3Σ−g transition is both electric dipole and spin forbid-den, the A band Einstein coefficient is extremely low. It has been determined
Vibrational levels Center [cm−1] Center [nm]
A Band 0←0 13122 762.1
B Band 1←0 14526 688.4
γBand 2←0 15903 628.8
δBand 3←0 17250 579.7
Table 6.4:Classification of b1Σ+g ←X3Σ−g transitions in molecular oxygen.
92 BUFFER-GAS LOADING PROSPECTS FOR MOLECULAR OXYGEN
759 760 761 762 763 764 765 766 767 768
10-20 10-19 10-18
SpectralLineIntensity[MHz/cm-2]
Transition Wavelength [nm]
296 K LN LHe
R branch P branch
Figure 6.5:A-Band line intensities at different temperatures. The liquid nitrogen (LN) temperature is 77.36 K and the liquid helium temperature (LHe) 4.21 K. More detailed and additional quantitative information on the A band line parameters and properties is summarized in Appendix D.
by Schermaul et al. [105] toAfi= 0.08931 s−1, which is about 9 orders of magni-tude below that of the rubidium D2line, for instance. The corresponding natural linewidth of 14.21 mHz will thus hardly be directly observable and the homo-geneous width will always be dominated by pressure broadening. On average, it is around 2.58 MHz/mbar (FWHM) at room temperature [101].
Expected absorption coefficients are similarly low. The values summarized in Table 6.5 indicate that a detection sensitivity below 10−8/cm has to be available in order to detect trapped oxygen molecules with an initial number density of 1012cm−3 via the A band. In analogy to standard atom optics and BEC experiments, one might tend to implement fluorescence spectroscopy for this purpose. It is in fact favored by the low branching ratio of only 1/60 to the intermediate and long-lived a1∆g singlet state, as calculated from the respective Einstein coefficients [99]. Although fluorescence detection has been considered in this context previously [68], other results [106] indicate that non-radiative quenching of the excited state due to impurities is very likely to reduce the efficiency of this technique. Additionally, the cryogenic environment allows only limited optical access and thereby reduces the available solid angle for fluorescence pickup. It is thus concluded that fluorescence detection of O2 is not suited for our purposes.
From the numerous alternative techniques, cavity-based methods are among the few easily reaching down into the expected range of absorption coefficients cited in Table 6.5 [61]. They appear to offer the best perspectives for an
imple-PERSPECTIVES 93
Temperature 296 K 77.36 K 4.21 K
Strongest transition R7Q8 R3Q4 R1Q2
Wavelength [nm] 760.8853888 761.4150430 761.7150174 Frequency [GHz] 394004.7508 393730.6739 393575.6171 Sif [MHz/cm−2] 2.648·10−19 5.661·10−19 3.367·10−18
Doppler width [MHz] 858.3 438.5 102.2
Peak absorption [%/cm] 2.898·10−8 1.213·10−7 3.094·10−6
Table 6.5: Strongest oxygen lines in different temperature regimes. Doppler broad-ening dominates in all cases. Peak absorption values have been calculated from(4.18) assuming a number density of 1012cm-3. They increase by two orders of magnitude when going from room temperature to 4 K.
mentation at cryogenic temperatures within the limited geometry of a buffer-gas loading experiment. The detection sensitivity is improved here over a di-rect absorption measurement by increasing the effective absorption path length through multiple reflections between the resonator mirrors. While the optical setup therefore stays quite compact, the internal power buildup reduces the re-quired power levels on the outside, thereby minimizing any absorptive heating of cryogenic optics. This in particular would allow to saturate trapped samples for sub-Doppler spectroscopy, even on relatively weak transitions.
6.3 Perspectives
Studies on cold and ultracold oxygen samples would in the first place help to gain understanding of the interactions between O2 molecules in particular and with other species in general. Theoretical predictions are usually based on calculated potential energy surfaces (PESs), which could be fine tuned with actual measurement results, e. g. loss rates of the individual isotopomers in the presence of a helium buffer-gas. The observation of collisions and even chemi-cal reactions under the well-defined conditions at ultracold temperatures could furthermore improve the understanding of thermochemistry in other regimes, where oxygen is the dominant molecule and thus of intense chemical interest.
Also, buffer-gas cooled but still untrapped oxygen samples could serve to improve spectroscopic data and the understanding of molecular structure. Preci-sion spectroscopy on selected species might even put new limits on fundamental theories. It is for example conceivable to reveal potential violations of the sym-metrization postulate by looking for forbidden transitions in buffer-gas cooled
16O2, thereby extending previous room-temperature experiments by de Angelis et al. [14] and Gianfrani et al. [107].
Once trapping is successful, it will of course be very interesting to evapora-tively cool oxygen molecules into the quantum degenerate regime and possibly create a ground-state molecular BEC for the first time. As pointed out in the introduction, such a quantum gas would be expected to show an unusual
be-94 BUFFER-GAS LOADING PROSPECTS FOR MOLECULAR OXYGEN havior due to the additional rotational and vibrational degrees of freedom. In this context it is also interesting to note that16O18O should have a minute elec-tric dipole moment [95]. The resulting dipolar interaction could for example be tuned by a sufficiently high external electric field and would have an observable effect on collective oscillation modes of the condensate [108].